Generalizations of a discrete universality theorem for Hurwitz zeta-functions

It is well known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that the shifts ζ(s + iτ ), t ? mathbbR tau in mathbb{R} (continuous case), and ζ(s + imh), m ? mathbbN è{ 0 } m in mathbb{N} cup left{ 0 right} , with fixed h > 0 (discrete case) approximate any analytic function. In the paper, the discrete universality is extended for some classes of the functions F(ζ(s, α)).